On Wed, 21 Nov 2007, chuck009 wrote:
> The Laplace Transform integral seems not to converge for any s for the function f(x)=1/x but LaplaceTransform returns -EulerGamma-Log(s) for this function:
>
>
> LaplaceTransform[1/x, x, s]
> Integrate[1/(x*Exp[s*x]), {x, 0, Infinity}]
>
> Is this a bug?
>
Hello,
The answer returned by LaplaceTransform in the above example is incorrect
and this example should return unevaluated.
The problem appears to be caused by the setting GenerateConditions ->
False with which the integral is computed by LaplaceTransform. With this
setting, Integrate attempts to regularize the divergent integral. Hence
a workaround for the problem is to use GenerateConditions -> True in
this case, as shown below.
================================
In[1]:= $Version
Out[1]= 6.0 for Linux x86 (32-bit) (June 28, 2007)
In[2]:= LaplaceTransform[1/x, x, s, GenerateConditions -> True] // InputForm
1
Integrate::idiv: Integral of ------ does not converge on {0, Infinity}.
s x
E x
Out[2]//InputForm= LaplaceTransform[x^(-1), x, s, GenerateConditions -> True]
=============================
Thank you for reporting the problem. We are sorry for the inconvenience
caused by it.
Sincerely,
Devendra Kapadia,
Wolfram Research, Inc.